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000881536.Pdf (3.344Mb) UNIVERSIDADE ESTADUAL PAULISTA "JÚLIO DE MESQUITA FILHO" CAMPUS DE GUARATINGUETÁ TIAGO FRANCISCO LINS LEAL PINHEIRO Estudo da sailboat para sistemas binários Guaratinguetá 2016 Tiago Francisco Lins Leal Pinheiro Estudo da sailboat para sistemas binários Trabalho de Graduação apresentado ao Conselho de Curso de Graduação em Bacharel em Física da Faculdade de Engenharia do Campus de Gua- ratinguetá, Universidade Estatual Paulista, como parte dos requisitos para obtenção do diploma de Graduação em Bacharel em Física . Orientador: Profo Dr. Rafael Sfair Guaratinguetá 2016 Pinheiro, Tiago Francisco Lins Leal L654e Estudo da sailboat para sistemas binários / Tiago Francisco Lins Leal Pinheiro– Guaratinguetá, 2016. 57 f.: il. Bibliografia: f. 53 Trabalho de Graduação em Bacharelado em Física – Universidade Estadual Paulista, Faculdade de Engenharia de Guaratinguetá, 2016. Orientador: Prof. Dr. Rafael Sfair 1. Planetas - Orbitas 2. Sistema binário (Matematica) 3. Metodos de simulação I. Título . CDU 523. DADOS CURRICULARES TIAGO FRANCISCO LINS LEAL PINHEIRO NASCIMENTO 03/06/1993 - Lorena / SP FILIAÇÃO Roberto Carlos Pinheiro Jurema Lins Leal Pinheiro 2012 / 2016 Bacherelado em Física Faculdade de Engenharia de Guaratin- guetá - UNESP 2011 Bacherelado em Engenharia de Produção Centro Universitário Salesiano de São Paulo - UNISAL 2008 / 2010 Ensino Médio Instituto Santa Teresa AGRADECIMENTOS Em primeiro lugar agradeço a Deus, fonte da vida e da graça. Agradeço pela minha vida, minha inteligência, minha família e meus amigos, ao meu orientador, Prof. Dr. Rafael Sfair que jamais deixou de me incentivar. Sem a sua orientação, dedicação e auxílio, o estudo aqui apresentado seria praticamente impossível. aos meus pais Roberto Carlos Pinheiro e Jurema Lins Leal Pinheiro, e irmãos Maria Teresa, Daniel, Gabriel e Rafael, que apesar das dificuldades enfrentadas, sempre incentivaram meus estudos. às funcionárias da Biblioteca do Campus de Guaratinguetá pela dedicação, presteza e principal- mente pela vontade de ajudar, aos funcionários da Faculdade de Engenharia do Campos de Guaratinguetá pela dedicação e alegria no atendimento. Este trabalho contou com o apoio da seguinte entidade: CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico RESUMO A sailboat é uma região estável de partículas localizadas entre a órbita de Plutão e Caronte. Ela possui características muito peculiares e foram estudadas minuciosamente por Winter et al. (2014) com o objetivo de descobrir quais os riscos esta região poderia trazer para a missão New Horizons. Os autores confirmaram a estabilidade da sailboat através de superfícies de seção de Poincaré. Para um entendimento mais profundo da sailboat, neste trabalho foram criados sistemas binários hipotéticos. Estabelecendo a massa (mp) e raio (rp) do corpo primário são iguais a de Plutão e variou-se a razão de massa do sistema, no intervalo µ = [0.05,0.70]. No corpo secundário o raio utilizado foi idêntico ao de Caronte rs = 610 km com órbitas circulares ou excêntrica, dependendo da simulação. Para a distância de separação dos dois corpos (d), também foi adotado a mesma do sistema Plutão-Caronte. As simulações numéricas foram feitas utilizando o integrador Radau 15 (EVERHART, 1985), onde considerou-se que as partículas (sem massas) sofrem a perturbação do binário mas não alteram a órbita dos corpos massivos. O tempo de integração adotado foi de 104 períodos orbitais (6500 dias, o mesmo da binária Plutão-Caronte). Os resultados das simulações mostraram que a existência desta região se limita a µ entre 0.05 e 0.27, esta região é formada inicialmente além de 0:5d, porém se aproxima do corpo primário a medida que µ cresce. Quando a razão de massa está entre 0.28 e 0.29 duas novas regiões estáveis surgem, uma situada além de 0:6d e se estende a distância superior a 0:8d e outra região localizada em aproximadamente 0:45d e de partículas com alta excentricidade, acima 0.6. Com um pequeno aumento na razão de massa estas duas regiões se misturam com a sailboat, formando uma única região. As simulações mostram também que pequenos incrementos na excentricidade do corpo secundário causam uma redução significativa no tamanho desta região dentro diagrama de condições iniciais (a × e). O tamanho da sailboat possui um comportamento inversamente proporcional quando é relacionado µ com a inclinação máxima das partículas. Os resultados mostram que esta região existe dentro de dois intervalos estreitos de ! (ao redor de 0◦ e 180◦) onde sua extensão é máxima. PALAVRAS-CHAVE: Sistemas Binários. Região Estável. Elementos Orbitais. ABSTRACT The sailboat is a stable region of particles located between the orbits of Pluto and Charon, this region has perculiar features and were studied in detail by Winter et al. (2014) with the goal to discover what the risk this region could cause for the New Horizons’s mission. The authors checked the stability of the sailboat through the Poincaré surface of scetion. To a deepier understanding of the sailboat, in this project has been created hypothetical binary systems. Setting the mass (mp) and radius (rp) of the primary body equals to Pluto. Varying the mass ratio of the system, since µ = [0.05,0.70], in the second body the radius adopted was identical to the Charon rs = 610 km and it had a circular or eccentric orbit, depending of the simulation. The separation distance (d) between two bodies was adopted the same of Pluto-Charon system. We numerically integrated the orbits using the Radau 15 (EVERHART, 1985), where it was considered that the massless particules were disturbed by the binary but it can’t change the orbit of massive bodies. The time span adopted was 104 orbital periods (6500 days, the same as the binary Pluto-Charon). The results of the simulation showed that the existence of this region is limited within µ between 0.05 and 0.27, this region is initially formed beyond to 0:5d, however, it get closer to the primary body when the µ grows. When a mass ratio is between 0.28 and 0.29 two new stable regions arised, one situated beyond 0:6d and extends to a distance greater than 0:8d and another region located at approximately 0:45d, but has high eccentricity, above 0.6. With a small increase in mass ratio these two regions mixed with a sailboat, forming a single region. The simulations show that small increments in eccentricity of the secondary body cause a significant reduction in the size of this region in the initial condition diagram (a × e). The size of the sailboat has a behavior inversely proportional when it is related µ and the maximum inclination of the particles. The results show that this region exists within two narrows intervals of ! (around of 0◦ and 180◦) where its extension is maximum. KEYWORDS: Binary Systems. Stable Region. Orbital Elements. LISTA DE ILUSTRAÇÕES Figura 1 Diagrama de condições iniciais estáveis (a × e) para o caso plano mostrando a sailboat....................................... 16 Figura 2 Distribuição dos sistemas estelares binários catalogados (µ × a=rp). 19 Figura 3 Regiões de estabilidades (em azul) para sistemas binários hipotéticos com razão de massa entre 0.05 até 0.10. 24 Figura 4 Regiões de estabilidades (em azul) para sistemas binários hipotéticos com razão de massa entre 0.11 até 0.16. 25 Figura 5 Regiões de estabilidades (em azul) para sistemas binários hipotéticos com razão de massa entre 0.17 até 0.22. 26 Figura 6 Regiões de estabilidades (em azul) para sistemas binários hipotéticos com razão de massa entre 0.23 até 0.28. 27 Figura 7 Regiões de estabilidades (em azul) para sistemas binários hipotéticos com razão de massa entre 0.29 até 0.34. 28 Figura 8 Excentricidade do corpo secundário máxima onde existe a sailboat pela razão de massa do sistema binário hipotético . 29 Figura 9 Diagrama de condições iniciais (a x e) para o caso plano e µ = 0.05 para sistemas com diferentes valores de excentricidade do corpo secundário, em verde as partículas que colidiram, em vermelhos as partículas que escaparam e em preto as partículas temporariamente estáveis. 30 Figura 10 Diagrama de condições iniciais (a x e) para o caso plano e µ = 0.11 para sistemas com diferentes valores de excentricidade do corpo secundário, em verde as partículas que colidiram, em vermelhos as partículas que escaparam e em preto as partículas temporariamente estáveis. 31 Figura 11 Diagrama de condições iniciais (a x e) para o caso plano e µ = 0.27 para sistemas com diferentes valores de excentricidade do corpo secundário, em verde as partículas que colidiram, em vermelhos as partículas que escaparam e em preto as partículas temporariamente estáveis. 31 Figura 12 Gráfico da inclinação máxima das partículas onde existe a sailboat pela razão de massa do sistema binário hipotético. 32 Figura 13 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.05 e 0.07. 33 Figura 14 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.08 e 0.10. 34 Figura 15 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.11 e 0.13. 34 Figura 16 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.14 e 0.16. 35 Figura 17 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.17 e 0.19. 35 Figura 18 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.20 e 0.22. 36 Figura 19 Diagrama de condições iniciais (a x e) para o caso com inclinação de 40◦, 80◦ e de inclinação máximo, com µ entre 0.23 e 0.25.
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